High-Frequency Quoting: Measurement, Detection and Interpretation Joel Hasbrouck 1

Outline  Background  Look at a data fragment  Economic significance  Statistical modeling  Application to larger sample  Open questions 2

Economics of high-frequency trading  Absolute speed  In principle, faster trading leads to smaller portfolio adjustment cost and better hedging  For most traders, latencies are inconsequential relative to the speeds of macroeconomic processes and intensities of fundamental information.  Relative speed (compared to other traders)  A first mover advantage is extremely valuable.  Low latency technology has increasing returns to scale and scope.  This gives rise to large firms that specialize in high-frequency trading. 3

Welfare: “HFT imposes costs on other players”  They increase adverse selection costs.  The information produced by HFT technology is simply advance knowledge of other players’ order flows.  Jarrow, Robert A., and Philip Protter,  Biais, Bruno, Thierry Foucault, and Sophie Moinas,

Welfare: “HFT improves market quality.”  Supported by most empirical studies that correlate HF measures/proxies with standard liquidity measures.  Hendershott, Terrence, Charles M. Jones, and Albert J. Menkveld, 2010  Hasbrouck, Joel, and Gideon Saar, 2011  Hendershott, Terrence J., and Ryan Riordan,

“HFTs are efficient market-makers”  Empirical studies  Kirilenko, Andrei A., Albert S. Kyle, Mehrdad Samadi, and Tugkan Tuzun, 2010  Menkveld, Albert J., 2012  Brogaard, Jonathan, 2010a, 2010b, 2012  Strategy: identify a class of HFTs and analyze their trades.  HFTs closely monitor and manage their positions.  HFTs often trade passively (supply liquidity via bid and offer quotes)  But …  HFTs don’t maintain a continuous market presence.  They sometimes trade actively (“aggressively”) 6

Positioning  We use the term “high frequency trading” to refer to all sorts of rapid-paced market activity.  Most empirical analysis focuses on trades.  This study emphasizes quotes. 7

High-frequency quoting  Rapid oscillations of bid and/or ask quotes.  Example  AEPI is a small Nasdaq-listed manufacturing firm.  Market activity on April 29, 2011  National Best Bid and Offer (NBBO)  The highest bid and lowest offer (over all market centers) 8

9 National Best Bid and Offer for AEPI during regular trading hours

Caveats  Ye & O’Hara (2011)  A bid or offer is not incorporated into the NBBO unless it is 100 sh or larger.  Trades are not reported if they are smaller than 100 sh.  Due to random latencies, agents may perceive NBBO’s that differ from the “official” one.  Now zoom in on one hour … 10

11 National Best Bid and Offer for AEPI from 11:00 to 12:10

12 National Best Bid and Offer for AEPI from 11:15:00 to 11:16:00

13 National Best Bid and Offer for AEPI from 11:15:00 to 11:16:00

14 National Best Bid for AEPI: 11:15: to 11:15: (400 ms)

So what?  HFQ noise degrades the informational value of the bid and ask.  HFQ aggravates execution price uncertainty for marketable orders.  And in US equity markets …  NBBO used as reference prices for dark trades.  Top (and only the top) of a market’s book is protected against trade-throughs. 15

“Dark” Trades  Trades that don’t execute against a visible quote.  In many trades, price is assigned by reference to the NBBO.  Preferenced orders are sent to wholesalers.  Buys filled at NBO; sells at NBB.  Crossing networks match buyers and sellers at the midpoint of the NBBO. 16

Features of the AEPI episodes  Extremely rapid oscillations in the bid.  Start and stop abruptly  Possibly unconnected with fundamental news.  Directional (activity on the ask side is much smaller) 17

A framework for analysis: the requirements  Need precise resolution (the data have one ms. time-stamps)  Low-order vector autoregression?  Oscillations: spectral (frequency) analysis?  Represent a time series as a combination sine/cosine functions.  But the functions are recurrent over the full sample.  AEPI episodes are localized. 18

Stationarity  The oscillations are locally stationary.  Framework must pick up stationary local variation …  But not exclude random-walk components.  Should identify long-run components as well as short-run. 19

Intuitively, I’d like to …  Use a moving average to smooth series.  Implicitly estimating the long-term component.  Isolate the HF component as a residual. 20

Alternative: Time-scale decomposition  Represent a time-series in terms of basis functions (wavelets)  Wavelets:  Localized  Oscillatory  Use flexible (systematically varying) time-scales.  Accepted analytical tool in diverse disciplines.  Percival and Walden; Gencay et. al. 21

Sample bid path 22

First pass (level) transform 23 Original price series 2-period average 1-period detail

First pass (level) transform 24 Original price series 2-period average 1-period detail 1-period detail sum of squares

Second pass (level) transform 25 2-period average 2-period detail 4-period average

Third level (pass) transform 26 4-period average 4-period detail 8-period average

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Interpretation 28

Multi-resolution analysis of AEPI bid 29

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31 1-4ms 8ms-1s 2s-2m >2m Time scale

Connection to standard time series analysis 32

The wavelet variance of a random-walk 33

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The wavelet variance for the AEPI bid: an economic interpretation  Orders sent to market are subject to random delays.  This leads to arrival uncertainty.  For a market order, this corresponds to price risk.  For a given time window, the cumulative wavelet variance measures this risk. 35

Timing a trade: the price path 36

Timing a trade: the arrival window 37

The time-weighted average price (TWAP) benchmark 38 Time-weighted average price

Timing a trade: TWAP Risk 39 Variation about time-weighted average price

Price uncertainty 40

The wavelet variance: a comparison with realized volatility 41

Data sample  100 US firms from April 2011  Sample stratified by equity market capitalization  Alphabetic sorting  Within each market cap decile, use first ten firms.  Summary data from CRSP  HF data from daily (“millisecond”) TAQ 42

Median Share price, EOY 2010 Mkt cap, EOY, 2010, $Million Avg daily dollar vol, 2010, $Thousand Avg daily no. of trades, April 2011 Avg daily no. of quotes, April 2011 Full sample $ ,1401,11123,347 Dollar Volume Deciles 0 (low) $ $ ,275 2 $ ,309 3 $ ,40515,093 4 $ , ,433 5 $ ,0771,23334,924 6 $26.341,3395,6012,04537,549 7 $28.401,86313,2363,21952,230 8 $36.733,46234,1197,24394,842 9 (high) $ ,352234,48325,847368,579

Computational procedures 44

Example: AAPL (Apple Computer) 45

46 Median99 th percentileMedian BidAskBidAsk 1 ms ms ms ms ms sec sec sec

47 Median 99 th percentile 1 ms ms ms ms ms sec sec sec

48 Median 99 th percentile 1 ms ms ms ms ms sec sec sec

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How closely do the wavelet variances for AAPL’s bid correspond to a random walk? 50 Scale Wavelet variance estimate Random-walk variance factors Implied random- walk variance 1 ms ms ms ms ms sec sec sec ,

Reasonable? 51

Volatility Signature Plots  Suggested by Andersen and Bollerslev.  Plot realized volatility (per constant time unit) vs. length of interval used to compute the realized volatility.  Basic idea works for wavelet variances.  “How much is short-run quote volatility inflated, relative to what we’d expect from a random walk?” 52

Normalization of wavelet variances 53

For presentation … 54

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The take-away  For high-cap firms  Wavelet variances at short time scales have modest elevation relative to random- walk.  Low-cap firms  Wavelet variances are strongly elevated at short time scales.  Significant price risk relative to TWAP. 56

Sample bid-ask wavelet correlations  These are already normalized.  Compute quintile averages across firms. 57

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How closely do movements in the bid and ask track? 59

A gallery  For each firm in mkt cap deciles  6, I examined the day with the highest wavelet variance at time scales of 1 second and under.  HFQ is easiest to see against a backdrop of low activity.  Next slides … some examples 60

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Conclusions  High frequency quoting is a real (but episodic) fact of the market.  Time-scale decompositions are useful in measuring the overall effect.  … and detecting the episodes  Remaining questions … 68

Why does HFQ occur?  Why not? The costs are extremely low.  Testing?  Malfunction?  Interaction of simple algos?  Genuinely seeking liquidity (counterparty)?  Deliberately introducing noise?  Deliberately pushing the NBBO to obtain a favorable price in a dark trade? 69